Certainly you can. Why ever not? It is simple; however, there are a few things to keep in mind for successfully preparing sunny-side-up eggs.
First off, be sure your eggs are fresh. As eggs age, the dense layer of white which surrounds the yolk thins out and the yolk is no longer as centered as it is in a fresh egg. By three weeks, the yolk flattens out and the white becomes uniformly watery. Eggs this old won’t fry up nicely. They’re edible, but not attractive, and the yolk is much more likely to break.
Yolks and whites coagulate at different temperatures, whites cooking faster than yolks. The trick is to get the yolk to the desired degree of firmness without making the white rubbery. This requires gentle heat. Because in a frying pan the heat is being applied to the bottom of the egg, too high heat will result in the bottom of the egg becoming tough or even burned while the top remains undercooked. The heat should be high enough that the egg begins to firm up as soon as it makes contact with the pan, but low enough not to cook too quickly.
There a couple of methods I use, depending on what kind of fat I have and how much of it there is. If you don’t mind using a fair amount (remember, while some may remain on the surface, the egg doesn’t absorb that fat), try this. For frying a couple of eggs, melt enough butter or bacon fat in an 8″ skillet to form a ⅛” to ¼” layer. Have the heat on medium low. Break the eggs and holding them as close as possible to the skillet, ease them into the pan. Cook until they’ll slide when you move the skillet back and forth. Then tilt the pan to one side and scoop up a spoonful of fat to baste the yolks with. Continue spooning and basting until the yolks film over. I’ve always found it fascinating that a bright yellow yolk turns a pale ivory/pink shade when the thin layer of white surrounding it coagulates.
If the skillet is crowded, it may be difficult to dip a spoon into the cooking fat. If that’s a problem, simply heat more fat in a small pan to use for basting. Be sure it’s good and hot or it won’t set the yolks. The heat under the pan shouldn’t be too hot, but it’s OK if the basting fat is.
If you prefer to use less fat, preheat the pan and add about 1-2 tablespoons worth. Break in the eggs, and cover the pan with a lid. This reflects the heat downward to cook the top side of the eggs. Sometimes I add a drop or two of boiling water to create a little steam, which also helps cook the tops. Only use a tiny amount, though. You don’t want the eggs to start simmering.
There you have it, eggs sunny-side-up. If you want them over easy, simply ease a spatula under each egg until it’s supporting as much of the egg as possible, including the yolk, and gently turn it. It should only take 10 seconds or so to finish cooking that side. Turn again, and serve immediately. Total cooking time is about four minutes, depending on hard you like the yolk cooked.